KR19980028549A - Feed-back automatic thickness control device and method of designing the filter - Google Patents

Abstract

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a feed-back thickness control apparatus and a filter design method that can reduce a plate thickness deviation by constituting a low-pass filter between a feed thickness controller and an output thickness gauge. In the filter design method of the present invention, the transfer function of the exit plate thickness is obtained, the transfer function of the exit plate thickness including the time delay is obtained, the time constant including the time delay is obtained by obtaining the pure time constant, And designing a low-pass filter using the bandwidth as a cut-off frequency of the low-pass filter. The control device of the present invention comprises a winder for winding a steel sheet, a rolling device for rolling the steel sheet output from the winder, An output thickness gauge for measuring the thickness of the steel sheet output from the first stand; and an output thickness gauge for measuring the thickness of the steel sheet fed from the first stand, The output of the first stand and the output thickness gauge is faster than the delay time existing between the first stand and the output thickness gauge And a feed-back automatic thickness controller for controlling a roll gap using a signal from the low-pass filter to improve the performance of the feed back automatic thickness controller, The deviation can be reduced.

Description

Feed-back automatic thickness control device and method of designing the filter

[0001] The present invention relates to a cold-rolled steel sheet thickness control apparatus in a cold rolling process, and in particular, to control a high-frequency exit plate thickness deviation signal that can not be controlled, A feed back automatic thickness control device capable of reducing the plate thickness deviation by improving the performance of the feed back automatic thickness controller by controlling the roll gap by forming a low pass filter (LPF) at the entrance of the back automatic thickness controller, and And a filter design method thereof.

In general, in an automated continuous cold rolling, a thickness control system is known as one of the cold rolling control models for rolling a base material to a desired plate thickness. This thickness control system model dynamically formulates the physical phenomenon of the cold rolling process It is composed of various theoretical formulas.

To set the initial roll gap, set the following:

P = f (H, h, t f, t b)

f = f (H, h, t f, t b)

h = P / k + s

Where P is the rolling load, f is the advance rate, H is the inlet thickness,

h is the exit side thickness, t _f is the front tension, t _b is the back tension

s is the initial gap of the rolling roll

If the model of the thickness control system is derived by setting the rolling load P and the advanced rate f as shown in the above equation and then partially differentiating the expressions, the following expression is obtained.

The thickness control system model described above is expressed in the form of a differential equation of a matrix, typically through the following roll parameters: roll gap, roll speed, and forward tension.

_{X i = A i-1 X} i-1 + A i X i + A i + 1 X i + 1 + B i U i + E i W i + E i + 1 W i + 1 ...... (1a)

Y _i = C _i-1 X _i-1 + C _i X _i + F _i W _i (1b)

(Where X = [dS, dVr, dtf] ^T = [roll interval, roll speed, front tension] ^T

U = [dS, dVr] ^T = [roll interval, roll speed] ^T

E = [dH, dk, dSr] ^T = [Inlet Thickness, Deformation Resistance, Roll Eccentricity] ^T

Y = [dh, dtf] ^T = [output thickness, front tension] ^T )

In the equations (1a) and (1b), the subscript _i represents the _i- th stand, _{i + 1} represents the influence of the _{i + 1 st} stand on the _i- th stand, A represents the system matrix B is a control matrix according to the control variable vector U, and E is a disturbance matrix according to the disturbance variable vector W.

And C and F are output matrices according to the state variable and the disturbance variable, respectively.

These matrices are determined from the specifications and dynamic characteristics of the rolling mill. When the thickness control system model equations (1a) and (1b) are integrated with respect to time, the state variables during rolling, In the same direction.

The thickness control model in the form of the equations (1a) and (1b) is based on the multivariable control theory and is most commonly used for the mass flow plate thickness control (MASS FLOW AGC) and the optimum control.

A set-up system is used to determine the initial values of the roll speed and the roll gap in order to obtain the target thickness by rolling the base material using the above rolling theory and the adaptive correction factor. However, it is impossible to obtain the target plate thickness only by the set-up system because of fluctuation of plate thickness variation of the base material and disturbance of the rolling mill itself.

Therefore, an automatic thickness controller is attached for rolling the base material to the target plate thickness in response to such disturbance factors. Among many automatic thickness controllers, there is a feedforward automatic gauge control (FF AGC) that controls the roll gap using an input thickness gauge, and a feed back automatic thickness controller (FF AGC) that controls the roll gap using an output thickness gauge FB AGC (feedback automatic gauge control).

The feed back automatic thickness controller operates to remove the plate thickness deviation by adjusting the roll gap using the following equation (1) when the target plate thickness deviation signal is measured from the output thickness meter installed at the exit plate thickness.

_

dH _FB : Roll gap control amount by feed-back automatic thickness control, dh: Deviation of output plate thickness

M: plasticity factor, K: elastic modulus, C _P : proportional gain constant, C _I : integral gain constant, S: Laplace operator

Typically, Equation (1) is implemented in a PLC (pro grammable logic controller) derived from the rolling theoretical equation and directly drives the roll gap. In addition, feed - back automatic thickness controllers have a large effect on the deviation of the outboard thickness compared to other automatic thickness controllers. Since M and K are determined as eigenvalues in Equation (1) and the feed back automatic thickness controller is constituted by a proportional integral (PI) controller, C _P and C _I depend on the rolling characteristics and the roll gap capability You have to decide.

1 is a schematic view of a conventional feed back automatic thickness control apparatus.

1, in the conventional feed back automatic thickness control apparatus, since the exit thickness gauge 5 is located between the first stand 2 and the second stand 3 rather than directly under the roll, there is always a time delay , And the proportion integral controller (PI) can not sufficiently exhibit their performance. In particular, when the gain is increased for a disturbance faster than the time delay of the feedback automatic thickness control device 7 itself, the system tends to become unstable.

In such a conventional technique, there is always a time delay. Even if the output thickness gauge 5 senses the disturbance, other disturbances are detected before transmitting the detection signal to the feedback automatic thickness control device 7, the proportion integral can not sufficiently show the performance of the controller.

In particular, it is necessary to reduce the gain in order to prevent the disturbance, that is, the high frequency, faster than the time delay of the feed back automatic thickness control device itself and to prevent the control of the controller from diverging, and when the gain is increased, the system becomes unstable have.

The present invention has been made to solve the above problems and to achieve improvements. Therefore, it is an object of the present invention to provide a low pass filter (hereinafter referred to as " low pass filter ") installed at the mouth of a feed back automatic thickness control apparatus in order to remove, in advance, LPF (Low Pass Filter).

It is still another object of the present invention to provide a feed back automatic thickness control apparatus and a feed back automatic thickness control apparatus, And to provide an automatic thickness control apparatus.

As a technical means for accomplishing the object of the present invention, a filter design method of a feed back automatic thickness control apparatus according to the present invention includes a step of obtaining a transfer function of an exit side thickness, Obtaining a transfer function of the output thickness including a time delay from a transfer function of the plate thickness and a transfer function of the plate thickness of the exit plate; obtaining a pure time constant from a graph of a transfer function of the exit plate thickness including the time delay, And designing a low-pass filter using the bandwidth as a cut-off frequency of the low-pass filter, wherein the low-pass filter includes a time constant including a time delay, The feed-back automatic thickness control apparatus using the filter according to the present invention comprises a winder for winding a steel sheet, A thickness measuring device for measuring the thickness of a steel strip to be unwound from the take-up machine at a first stand, and an output thickness measuring device for measuring a thickness of the steel strip from the first stand, A low pass filter for removing an output thickness deviation signal of a period longer than a delay time existing between the first stand and the output thickness gauge from the signals output from the output thickness gauge, And a feed-back automatic thickness controller for controlling the roll gap using a signal from the feed-back automatic thickness controller, thereby reducing the plate thickness deviation by improving the performance of the feed-back automatic thickness controller.

1 is a schematic view of a conventional feed back automatic thickness control apparatus,

2 is a schematic view of a feed back automatic thickness control apparatus using a filter according to the present invention,

3 is a graph showing the time response of a conventional feed back automatic thickness control apparatus,

FIG. 4 is a graph showing the deviation of the thickness of the exit side of a conventional feedback control automatic thickness control apparatus without using a filter,

FIG. 5 is a graph showing the deviation of thickness of the exit side plate of the feed back automatic thickness control apparatus using the filter according to the present invention.

DESCRIPTION OF THE REFERENCE NUMERALS

1: take-up machine 2: 1 stad

3: 2 std 4: Inside thickness meter

5: Output thickness meter 6: Feed-forward automatic thickness controller

7: feed-back automatic thickness controller 8: low-pass filter

Hereinafter, a configuration of a method for performing a filter designing method of a feed back automatic thickness control apparatus according to the present invention will be described. The filter design method of the feed back automatic thickness control apparatus according to the present invention uses the above-described thickness control system model equations (1a) and (1b)

_

G (S) is the transfer function of the exit plate thickness, dh is the deviation of the exit plate thickness, S is the Laplace operator

dH: roll gap control by feed-forward automatic thickness control and feed back automatic thickness control

a, b, c, d, e, f, g: coefficients varying according to the conditions of the automatic thickness control device

.

Next, a transfer function (G (S)) of the exit plate thickness is calculated from the transfer function G (S) of the exit plate thickness in consideration of the time delay (Td) (G '(S)).

G '(S) = G (S) e- ^TdS

G '(S) is the transfer function of the exit plate thickness including the time delay,

G (S) is the transfer function of the exit plate thickness, S is the Laplace operator, T _{d is the} time delay

(Ts) is obtained from a graph (see FIG. 3) showing a characteristic of a step input of a transfer function (G '(S)) of the exit plate thickness including the time delay to obtain a time constant The time constant (T) is obtained.

T = T _d + T _s

T: time constant, Td: time delay, Ts: pure time constant

The bandwidth (? _B ) in the frequency domain is obtained from the time constant (T) including the time delay by the following equation,

ω _B = _

ω _B : bandwidth, T: time constant

Using the bandwidth ([omega] _B ) as the cut-off frequency of the low-pass filter,

_

(F) S: transfer function of low-pass filter, S: Laplace operator, ω _B : bandwidth

And designing a low-pass filter.

Hereinafter, a configuration of a feedback automatic thickness control apparatus using the low pass filter according to the present invention will be described with reference to the accompanying drawings.

2 is a schematic view of a feed back automatic thickness control apparatus using a filter according to the present invention.

The automatic thickness control apparatus according to the present invention comprises a winder (1) for winding a steel plate, an inlet thickness gauge (4) for measuring the thickness of the steel plate unwound from the winder (1) An output thickness gauge 5 for measuring the thickness of the steel sheet from the first stand 2 and a thickness gauge 5 for measuring the thickness of the exit thickness gauge 5 A feed-forward automatic thickness controller 6 for controlling the roll gap using the inlet thickness gauge 4, a second stand 3 for rolling a steel sheet from the output thickness gauge 5, A low pass filter 8 for eliminating an outboard thickness deviation signal having a period higher than the delay time existing between the first stand 2 and the output thickness gauge 5 in the low pass filter 8, To control the roll gap using a signal from < RTI ID = 0.0 > Id bag consists of automatic thickness controller 7.

In the drawings referred to in the present invention, components having substantially the same configuration and function will use the same reference numerals.

The apparatus and method according to the present invention thus constructed will be described in detail below.

[Table 1]

_

From the conditions of Table 1, the transfer function of the outboard thickness for the roll gap is obtained by using the thickness control system model equations (1a) and (1b) described above and the transfer function G (s) 2 < / RTI >

_

G (S) is the transfer function of the exit plate thickness, dh is the deviation of the exit plate thickness,

dH: roll gap control amount by FF AGC and FB AGC, S: Laplace operator

The time delay (T _d ) of the plate from under the roll to the exit thickness gauge 5 of the first stand 2 is given as about 0.5 seconds from the condition of Table 1 above. That is, the time delay (T _d ) of the plate is obtained by dividing the distance from the roll right side to the exit side thickness gauge 5 of the first stand 2 by the rolling speed of Table 1 above.

Therefore, the conversion into a full charge function including the time delay in Equation (2) yields Equation (3).

G '(S) = G (S) e- ^0.5S

G '(S) is the transfer function of the exit plate thickness, including the time delay,

G (S) is the transfer function of the exit board thickness, S is the Laplace operator

When the time response characteristic is obtained by using the unit step which is the test input in the time domain using the above-mentioned Equation (3), it is displayed as shown in FIG. 3 is a graph showing a time response of a conventional feedback automatic thickness control apparatus. In FIG. 3, the net time constant Ts excluding the time delay is given as 0.17 seconds, so that the time constant T due to the time delay is represented by Equation 4 below. The time constant is the system response characteristic index, which is the time when the response reaches 63% of the steady state.

_{T = T d + T s =} 0.5 +0.17 = .67 cho

T: time constant, Td: time delay, Ts: pure time constant

The bandwidth (? _B ) in the frequency domain can be obtained by the following inequality (5) by taking the reciprocal of the time constant. If the bandwidth value is high, the response of the system is fast, and if it is small, the response is slow. That is, it is difficult for the system to react at frequencies higher than the bandwidth, and it may react well at lower frequencies.

_

ω _B : bandwidth, T: time constant

The frequency of the disturbance that can be removed by the apparatus according to Equation (5) is determined to be about 0.24 Hz or less, so that the low-pass filter is designed to pass only the lower frequency. In general, the first fundamental equation of the low-pass filter is expressed by Equation (6) below.

_

F (S): transfer function of the low-pass filter, S; Laplace operator, ω _B : bandwidth

The determined cutoff frequency 0.24 Hz is substituted for ω _B in Equation 6 and the filter is provided between the output thickness gauge 5 and the feed back thickness control device 7 as shown in FIG. 7 and the exit thickness gauge 5 to eliminate the exit board thickness deviation signal that is faster than the delay time existing between the feed thickness gauge 5 and the output thickness gauge 5, thereby improving the performance of the feed back automatic thickness control apparatus and reducing the plate thickness deviation. .

The effects of the present invention will be described in detail as follows.

The feed-back automatic thickness control using the filter according to the present invention was performed using the actual rolling conditions of Table 1 above. FIG. 4 is a graph showing the deviation of the thickness of the exit side of the feed back automatic thickness control system without using the conventional filter, and FIG. 5 is a graph showing the deviation of the exit side thickness of the feed back automatic thickness control system using the filter of the present invention to be. As shown in FIG. 5, it can be seen that the present invention has an effect of improving about ± 0.02% in the thickness deviation of the stand-off plate 1 compared with the conventional one.

As described above, according to the present invention, there is a table for reducing the plate thickness deviation by improving the performance of the feed back automatic thickness controller by removing the high frequency output plate thickness deviation signal which can not be controlled by the feed back automatic thickness controller in advance.

Claims (4)

In the filter design method of the feed back thickness control apparatus, the transfer function G (S) of the exit side thickness is obtained by a conventional automatic thickness control model construction method, and the time of the plate from the bottom of the roll to the exit side thickness gauge of the stand Obtaining a transfer function G '(S) of the exit plate thickness including a time delay from a delay T _d and a transfer function G (S) of the exit plate thickness; (T _s ) is calculated from the step input characteristics of the transfer function (G '(S)) of the stand and the time constant (T) including the plate time delay (T _d ) (? _B ) in the frequency domain from the time constant (T) including the time delay, and designing a low-pass filter having the bandwidth (? _B ) as the cut-off frequency. A feed-back automatic thickness feature Method of filter design of a speech device. The method of claim 1, wherein the pure time constant (Ts) is a response characteristic index of the system, and the time when the response reaches 63% of the steady state. A feed-back automatic thickness control apparatus comprising: a winder for winding a steel plate; a first stand for rolling a steel plate outputted from the winder; and an inlet thickness gauge for measuring the thickness of a steel plate unwound from the winder, An output thickness gauge for measuring a thickness of the steel sheet output from the first stand, and a second thickness gauge for measuring a thickness of the steel sheet output from the first thickness gauge for a period longer than a delay time between the first stand and the output thickness gauge And a feed back automatic thickness controller for controlling a roll gap by using a signal from the low pass filter. The apparatus as claimed in claim 3, wherein the low pass filter has a transfer function (G (S)) of a thickness of the exit plate including a delay time existing between the first stand and the exit thickness gauge from a transfer function (G'(S)) the time constant including the seek, the number of steps from the pure water constant input response (Ts) and the time delay (T _d) of the transfer function (G'(S)), including the time delay (T ) Is a low pass filter which obtains a bandwidth (? _B ) in a frequency domain from a time constant (T) including the time delay and sets the bandwidth (? _B ) as a cutoff frequency thereof. Device.